Question

Line OP has an equation of a line y = 6x − 5, and line QR has an equation of a line y = 6x + 3. These two equations represent

the same line
lines that are neither parallel nor perpendicular
parallel lines because the slopes of the lines are equal
perpendicular lines because the slopes are opposite reciprocals

Answer 1

Lines are parallel as slope are equal
m=6

Answer 2

Answer: The correct option is (C) parallel lines because the slopes of the lines are equal.

Step-by-step explanation: Given that the equation of line OP is

`y=6x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

and the equation of line QR is

`y=6x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

We are to select the correct statement about the two lines.

The slope-intercept of a straight line is given by

`y=mx+c,`

where m is the slope and c is the y-intercept of the line.

Comparing equations (i) and (ii) with the slope intercept form, we get

For line (i),

`\textup{slope, }m_1=6,~~~\textup{y-intercept,}c_1=-5.`

For line (ii),

`\textup{slope, }m_2=6,~~~\textup{y-intercept,}c_2=3.`

So, we get

`m_1=m_2,~~~c_1\\eq c_2.`

This implies that the slope of line OP is equal to the slope of line QR.

Sine the y-intercepts of the lines are not equal, so the lines cannot be same.

We know that if the slopes of two lines are equal, then the lines are parallel.

Thus, the given lines OP and QR are parallel because they have the same slope.

Option (C) is CORRECT.